Through Math for America, I am part of an on-going collaboration with the New York Times Learning Network. My latest contribution, a Test Yourself quiz-question, can be found here:
https://learning.blogs.nytimes.com/2012/04/02/test-yourself-math-april-2-2012/
This question is based on Fred Newman’s world record of 20,371 free throws in 24 hours. How fast was he making those shots?
Through Math for America, I am part of an on-going collaboration with the New York Times Learning Network. My latest contribution, a Test Yourself quiz-question, can be found here:
https://learning.blogs.nytimes.com/2012/02/27/test-yourself-math-feb-27-2012/
This problem is based on the unlikely emergence of basketball star Jeremy Lin. How unlikely was his inaugural 7-game winning streak?
After enjoying a well-contested Superbowl that seemed to appropriately represent the teams, the season, and the league in terms of the level of play and competitiveness, I started wondering about how the big game compares to regular season play. I wondered if teams performed better or worse, on average, given the pressure and scrutiny of the championship game.
I thought a simple place to start examining this question would be to look at Superbowl scoring versus regular season scoring. Below is a chart showing the difference (Superbowl Score – Average Regular Season Score) for all 46 Superbowls.
At the far right, we see the results of Superbowl 46: Giants 21, Patriots 17. The league average in scoring this years was 22 points per game, so the difference here is 38 – 44 = -6.
It seems as though it is more common for more points to be scored in the Superbowl than in an average regular season game. Unfortunately, there are a lot of stories one could tell about why that might be so: better teams (and therefore better offenses) make it to the Superbowl; defenses are more susceptible to pressures of the big game; the extra preparation time gives offensive coordinators and advantage.
So how could we more rigorously explore the quantitative characteristics of the Superbowl?
I have enjoyed analyzing and writing about the strategy implications of the NFL’s Playoff Overtime rules, and we’ve seen those rules in action for the first time this year.
Here’s a short summary: the first possession in overtime is determined by a coin flip. The first-possessing team will be known as Team A, and the other team will be Team B. If Team A scores a touchdown, they win immediately; if Team A scores a FG, then Team B will receive the ball and can win (with a TD), tie (with a FG), or lose (with a turnover). Aside from the specific first- and second-possession situations governed by these rules, the rest of overtime plays out in classic sudden-death style.
I looked closely at whether it is useful for Team A to attempt a FG, but the question that occurred to me recently was “If you win the coin toss, is it obvious that you want the ball first?”
Consider the following chart. Again, Team A is the first-possessing team, and Team B is the other team. The chart shows all the possible sequences of outcomes on the first two possessions: touchdown (TD), field goal (FG), or Turnover. Here, a turnover could be a fumble, and interception, a punt, or a turnover on downs.
The first-possessing team, Team A, certainly has an advantage in that they can end the game immediately by scoring a touchdown. But if they don’t score a touchdown, Team B can always win with a TD and in some cases can win with only a FG! Furthermore, as the original kickoff team, Team B may enjoy a strategic advantage in field position, which can further affect the above scenarios.
Now, in all situations where the game is not decided within the first two-possessions, Team A gets the ball first as sudden-death rules take over. However, I recall analyses that suggest that the first possessing team doesn’t have a statistically significant advantage in sudden-death overtime.
This is an admittedly elementary look at the situation, but it seems to me that the answer to the question “Do we want the ball first in OT?” is not obvious. Hopefully I’ve given the coaches something to think about this week.
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Through Math for America, I am part of an on-going collaboration with the New York Times Learning Network. My latest contribution, a Test Yourself quiz-question, can be found here:
https://learning.blogs.nytimes.com/2012/01/30/test-yourself-math-jan-30-2012/
This question is based on the late Joe Paterno’s record for major college football victories by a head coach. How many years would it take for a contemporary to catch him?